When the distinguished theoretical physicist Carlo Rovelli was a student, he didn't spend much time studying: he was too busy trying to overthrow the government. Bologna in 1977—and Italy throughout the decade—was a stage for intense political struggle, and the leading players were the extra-parliamentary groups of the New Left. With the Italian Communist Party in terminal decline, the New Leftists in Bologna occupied universities, fought fascists in the street and established autonomist communities. They were all, in their own way, oriented towards revolution. "It was very fragmented," says Rovelli, "some of us were Marxist-Leninist or Trotskyist; some were hippies into sex, drugs and rock'n'roll; and some were just into the mystical Far East."

Although Rovelli was involved with Metropolitani Indiani, a group of hippies who dressed like Native Americans and were "a lot more show than substance", his radicalism also found meaningful expression. He worked at Radio Alice, a subversive radio station that provided information for protesters, sparking riots when it announced the death of a student shot in the back by police. He also co-wrote a book about the so-called "Movement of 1977" called Fatti Nostri, made up of radio transcripts, political documents and zealous essays. The police tried to ban its publication and, after it was secretly printed, searched his parents' house and launched an investigation into the editors, which was eventually thrown out by a judge.

Ultimately the Movement of 1977 was a "totally failed revolution". Too many of its participants were the children of the bourgeoisie and had a "suspicion of any attempt to impose structure" on their action: its ephemerality was built-in. So, Rovelli left the barricades and began working out how to avoid spending the rest of his life in an of- fi ce job. ("It's funny," he adds, "now the problem for young people is to fi nd a job; in my generation the problem was how to not fi nd a job.") It was at this juncture that he "fell in love with science", seeing it as an ideological terrain "where revolutions actually succeed, revolutions in thinking".

But revolutions in theoretical physics are quieter than those in politics: once completed, public life carries on undisturbed. It took a century for the Copernican Revolution to leave the province of academia and become common knowledge. Likewise, the two physical revolutions of the last century that invalidated Newton's ruling ideas— Einstein's general relativity and Bohr's quantum mechanics—appear arcane to a contemporary audience. "If you go into any high school and ask students about space and time, you get an answer which is basically Newtonian," Rovelli explains. Our intuitions dictate that space is completely empty, time flows in a straight line, and gravity operates like a metaphysical force of attraction, but this hasn't reflected scientific understandings of the universe since Einstein, and it explains why Rovelli wrote Seven Brief Lessons on Physics. If Fatti Nostri was propaganda for a revolution manqué, Seven Brief Lessons on Physics is propaganda for the two revolutions, general relativity and quantum mechanics, that have passed us by.

It's his first book for a popular audience and has been a tremendous success in Italy: Sette Brevi Lezioni di Fisica sold 140,000 copies in six months, outselling 50 Shades of Grey for two months and surpassing the publisher's expectations. It has been translated into 24 languages and the English version, published by Allen Lane (Penguin) was released this October. When I meet Rovelli at Penguin's offices, he is friendly and inquisitive, asking straight away about the etymology of the word "Strand", the central London road running outside. (I didn't have an answer, but it turns out to be derived from an Old English word for a beach or shore, tied to the road's position parallel to the Thames.) He is short, carries a backpack and has black-and-grey curly hair that he fiddles with when in thought. Like the scientists he writes about in his book, he is decisively equivocal—alloying confi dence with doubt, qualifying assertions about the universe with "at least it seems to me..." Despite his success, it becomes clear he eschews the arrogance of those other public spokespeople for science—figures like Neil DeGrasse Tyson and Brian Cox—that the English-speaking world is obsessed with, which is a relief.

I jog his memory of the "failed revolution" of 1977 by presenting a pamphlet, titled Memories of A Metropolitan Indian, written by a participant— he peers at it before exclaiming, "Oh! My youth!" He reminisces fondly about his revolutionary days, so I ask whether he keeps in touch with his comrades. "Yes, I do. A surprising number of them live in the memory of it, which I think is totally stupid," he says. "The idea was we would change everything: get rid of family, cops and money... But you have to basically take the world as it is, changing it here and there." He might no longer be committed to a widescale political transformation of society, but traces of the student that was are visible in the book: the clearest sign of a radical mind in Seven Brief Lessons on Physics appears when Rovelli defi nes his research into the fringes of theoretical physics. "In the vanguard," he writes, "science becomes incandescent in the effort to imagine what has not yet been imagined." This reads less like science, I suggest, and more like the definition of utopian political thought. Rovelli is bemused but agrees. "It's funny you ask this because I don't usually talk about it. It's always in the background. There's an aspect of rebellion in my work that is definitely rooted in that ideology."

Seven Brief Lessons on Physics begins with the theory of general relativity. Einstein's revision of Newton's model of empty space and gravitational force is, Rovelli writes, "breathtakingly simple": the gravitational fi eld is not a magical force within space but is space itself. This picture is complicated by quantum theory, which holds that "electrons do not always exist" but only do so when they interact with something else. After lessons on the shape of the universe, the particles that compose it and the illusory nature of time, we learn about Rovelli's contribution to the fi eld: an attempt to resolve the contradictions between general relativity and quantum theory called "loop quantum gravity". This is where his work becomes animated by the utopian. As director of the Centre de Physique Théorique in Marseille, he has pioneered a theory that claims space is made up of minute "grains of space", interwoven like chainmail. When describing these grains of space with mathematical equations, the constant time—which is usually present in these calculations—is omitted: Rovelli's universe is literally timeless. "It is a huge conceptual leap," he says, one that he and colleagues reached "by avoiding the tendency in theoretical physics to follow the crowd".

The subject matter is complex but rendered in simple prose. The chapters are short, the book a mere 80 pages, and Rovelli says most of his time writing was spent editing: the content of a theory is reduced to its simplest proposition and the implications of its conclusion are given an elegant, philosophical gleam. But there are omissions and the reader is left wanting, such as on the emergence of the book's central characters. Although the book describes a time-less and space-less universe that transcends individuality, there are great individuals who populate it: the geniuses. It's a term Rovelli uses a lot, applying it to Einstein, Bohr, Maxwell and Heisenberg. The geniuses burn bright with hubris and doubt, increasing scientific knowledge in real terms but forever dissatisfied. Rovelli attempts, in line with that ideology of youthful rebellion, to explain where geniuses come from—"Einstein attended occasional lectures as a student for pleasure, without being registered or having to think about exams. It is thus that serious scientists are made"—but they remain mysterious creatures, so I ask how geniuses are made. Shouldn't a history of science look at the historical conditions of an era and how they contribute towards the emergence of breakthroughs rather than focusing on a few great men? Doesn't scientifi c knowledge have a sociohistorical character, operating within society like the rest of us?

He pauses for some time. He replies that it might be the case that there are certain ideas that "happen to coalesce" around certain individuals, but then hesitates: "But if that were true, how was it possible that Einstein did so many things? He didn't do one great thing, he did six or seven. So obviously he had the right tools." He's worried that emphasising the historical truth of a claim to knowledge leads to relativism, according to which one can't say what is objectively true. It's the first unsatisfying response that he's given in our time together, and he senses it. "Look," he adds, "Einstein developed special relativity, which is all about simultaneity, while working in a patent office on projects for French, German and Swiss trains that had the problem of synchronising their clocks between stations. So the technological problems of his time impacted his theory. Likewise, thermodynamics came out when people in England started making steam machines and were able to see heat in action. More than that, the entire ideology in your head affects the way you think about the world. But, with all this, you understand what heat is—and it remains true! You understand the earth is a sphere and it's not a sphere because feudalism went down, it's a sphere, period! Maybe it's true we understood it once we freed our minds from feudalism, but it remains a fact that it's a sphere, and it's going to be a sphere forever!"

Having made a world-renowned theoretical physicist explain to me that the Earth isn't fl at, I look down at my notes. There's one more topic scribbled and it's likely to cause as much discomfort: God. "In Italy," he says, "the Catholic religion is so dominant that I think people appreciate, in my book, a simple story and a plain way of understanding humanity without nonsense." But despite being a "rationalist atheist", Rovelli is sympathetic towards the divine: in the book he refers to space as "the heavens" ("An accurate translation" from the Italian edition, he assures me); and often presents cosmic concepts from a messianic perspective—sometimes denoted as "God", sometimes as a "hypothetical supersensible being"—to help the reader understand them. He resists my suggestion that his work leaves conceptual space for God ("No, no, it's just a way of explaining things!") but is not blind to the anti-intellectualism of contemporary atheism, telling me that he's "against the agenda of people like Richard Dawkins" who go around saying that everyone who believes in God is stupid. "Religiosity is part of who we are and there's nothing wrong with that." But when I ask, a few days later via e-mail, what he really thinks of the New Atheist trend, he is diplomatic to the point of parody: "I think it is good that ideas, good and bad, are made visible. Then people can listen, think, choose, develop..." The decorum, however, is understandable when I discover that he's sharing a stage with Dawkins at a public talk a few weeks later.

Hippie, revolutionary, theoretical physicist... I end by asking what he makes of his fourth career: public intellectual. Now that he tours the world delivering TED Talks, writes columns for Sunday newspapers and gives interviews to global punk conglomerates, has his vocation changed? Healthily, he is unimpressed by the prospect. "Writing books is not my job. What I really like and love in life is when I shut the door, turn off the internet and do my little calculations. That's when I'm happy," he replies. "Recently I've been doing too many..." he doesn't finish the sentence and smiles, possibly not wanting to offend the representative from Penguin who's just entered the room.

We finish the interview and try to leave Penguin's labyrinthine offices, getting lost more than once on our way out. I'm still thinking about the politics of his youth, as is he. He starts talking about Herbert Marcuse and the philosophers of the New Left he used to read. Marcuse taught him, he tells me, how people in the West were less free than those in the Soviet Union precisely because of the individual liberties they were indulged, blinding them to the social tyranny of the free market.

We part ways and I dodge tourists on the busy Strand—which, weeks before, had been busy in a different way, blocked by thousands marching towards parliament—thinking about how political convictions can change over a lifetime. I think of the disappointed radicals of Rovelli's generation who either live in nostalgia for an impossible revolution or have re-purposed their ideas to become pragmatic reformists. I think of the theoretical physicists applying principles of utopia to their work, not to imagine or create better worlds, but to more accurately describe the one we live in. It's a fascinating profession but I can't help feel it begs a political question, the kind Rovelli abandoned considering years ago: what's the point of describing the atomic structure of a world as squalid and senseless as ours?